Cauchy Combination Test: A Powerful Test With Analytic p-Value Calculation Under Arbitrary Dependency Structures

Yaowu Liu and Jun Xie

Journal of the American Statistical Association, 2020, vol. 115, issue 529, 393-402

Abstract: Abstract–Combining individual p-values to aggregate multiple small effects has a long-standing interest in statistics, dating back to the classic Fisher’s combination test. In modern large-scale data analysis, correlation and sparsity are common features and efficient computation is a necessary requirement for dealing with massive data. To overcome these challenges, we propose a new test that takes advantage of the Cauchy distribution. Our test statistic has a simple form and is defined as a weighted sum of Cauchy transformation of individual p-values. We prove a nonasymptotic result that the tail of the null distribution of our proposed test statistic can be well approximated by a Cauchy distribution under arbitrary dependency structures. Based on this theoretical result, the p-value calculation of our proposed test is not only accurate, but also as simple as the classic z-test or t-test, making our test well suited for analyzing massive data. We further show that the power of the proposed test is asymptotically optimal in a strong sparsity setting. Extensive simulations demonstrate that the proposed test has both strong power against sparse alternatives and a good accuracy with respect to p-value calculations, especially for very small p-values. The proposed test has also been applied to a genome-wide association study of Crohn’s disease and compared with several existing tests. Supplementary materials for this article are available online.

Date: 2020
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Citations: View citations in EconPapers (17)

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DOI: 10.1080/01621459.2018.1554485

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